Independence of hyperlogarithms over function fields via algebraic combinatorics

Details Independence of hyperlogarithms over function fields via algebraic combinatorics Independence of hyperlogarithms over function fields via algebraic combinatorics

2011-01-24

arxiv.org/abs/1101.4497v1

Mathematics

Combinatorics

Scientific paper

We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has only singularities of first order (Fuchsian-type equations) and this implies that they freely span a space which contains no primitive. We give direct applications where we extend the property of linear independence to the largest known ring of coefficients.

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